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This question involves the use of trigonometry in alternating current (AC) circuits, particularly focusing on the relationship between the applied voltage (\(V\)), the voltage across the resistor (\(V_R\)), and the voltage across the inductor (\(V_L\)), as well as the phase angle \(\phi\), which determines how much the current lags the applied voltage.

Given:
- Phase angle \(\phi = 18.6^\circ\)
- Applied voltage \(V = 243 \, \text{V}\)

To solve for \(V_L\) (the voltage across the inductor), we can use the relationship between these values in an AC circuit.

### Formula:
The total voltage in an AC circuit can be resolved into components based on the resistor and inductor voltages:
\[
\tan(\phi) = \frac{V_L}{V_R}
\]
But since we don’t know \(V_R\), we can instead use the following relationship involving the total voltage \(V\):
\[
V_L = V \sin(\phi)
\]

### Calculation:
Substituting the known values:
\[
V_L = 243 \times \sin(18.6^\circ)
\]

Let me calculate that for you.The voltage across the inductor \( V_L \) is approximately \( 77.51 \, \text{V} \).

Do you have any questions or need further details?

Here are some related questions to consider:
1. How is the phase angle \(\phi\) related to the impedance of a circuit?
2. What is the significance of the voltage across the resistor \(V_R\) in AC circuits?
3. How can we calculate the current in the circuit using the given voltage?
4. How does the inductive reactance affect the phase difference between current and voltage?
5. How would the calculation change if the phase angle \(\phi\) were larger or smaller?

**Tip:** Always make sure to convert angles to radians when using trigonometric functions in formulas.

Given that ϕ = 18.6° and v = 243 V, evaluate vL.

Learn how to calculate the voltage across an inductor (V_L) in an AC circuit where the phase angle ϕ is 18.6° and the applied voltage V is 243 V. This solution involves trigonometric functions and phase relationships in AC circuits. Suitable for students in Grades 11-12.

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